"The painter must leave the beholder something to guess," says Ernst Gombrich, and it's a response that comes to mind time and again in the galleries of Madrid. The quantity and quality of fine art on display has never been greater: all three institutions of its "art triangle" have been expanded in recent years. However, the splendours they contain are often enigmatic.

What makes this a unique moment in the capital's art life goes beyond paintings on walls: it's theatre, with the one-off uniting of Pablo Picasso's most "Spanish" image with a key body of work from his decades of exile. The two largest Picasso collections are in Barcelona and Paris, the artist having worked in France from the Spanish civil war till his death in 1973. But his one painting of great national significance - Guernica, the austere response to the attack on the Basque town by German bombers supporting General Franco in April 1937 - is housed in Madrid's Reina Sofía Museum, the location for Spain's collection of modern and contemporary art, in an 18th-century hospital building near Atocha Station.

Ample context for Guernica and the works that preceded it comes from the visiting collection of the artist's favourite works from Paris, while the museum there is being refurbished. The resulting synthesis of 400 works spanning his career provides a chance to appreciate his still-challenging achievement from a Spanish perspective (till May 5, 10am-9pm, except Sunday 10am-2.30pm, closed Tuesday).

The nearby Prado Museum, national home of art before the 20th century, also has the air of finally being able to go about things that it has always wanted to do. In April 2007, the Guardian's Jonathan Glancey found architect Rafael Moneo's extension to it to be "a quietly serious and beautifully crafted building that is as much a work of urban planning and undercover civil engineering as it is a work of art", and now it has fully come to life (9am-8pm, closed Monday).

From the ground floor entrance, escalators lead up to the restored cloister of the Hieronymite monastery where Philip II stayed on visits from the palace-monastery of El Escorial. Now it contains sculptures by Leone and Pompei Leoni of the Spanish king who came close to ruling Britain and his parents, Charles V and the Empress Isabella: there could be no more telling embodiment of a family ambitious to unite Europe under Catholic rule, with funds generated by the exploitation of the Americas.

'But where's the painting?' ... detail from Velázquez's Las Meninas. Photograph: The Gallery Collection/Corbis
It didn't happen, and so successive Hapsburg and Bourbon monarchs took solace in art and architecture, till the upheavals of the Napoleonic wars and the onset of deafness compelled Francisco Goya to abandon deference and produce the bleakest of images, unlocking the psyche for its great Spanish explorers of a century later - Gaudí, Picasso, Dalí and Miró.

At the centre of the 200 works that go to make up Goya in Times of War (till July 13) are his great firing-squad scene,
The Third of May 1808, and its companion showing the previous day's insurrection against the French forces occupying Madrid at the start of the war of independence that lasted till 1814. The conflict undergoes a stark dissection, notably in the prints of The Disasters of War.

As well as providing space for temporary exhibitions, the opening of the extension has left many of the celebrated paintings of the old Prado building displayed much better than previously. And undisturbed at its centre is Velázquez's masterpiece Las Meninas, making the spectactor wonder if he or she is really to take the place of the king and queen in front of the artist and the group from the royal household. Or as the poet Théophile Gaultier put it, "But where's the painting?"

According to Andrew Graham-Dixon in his recent BBC television series The Art of Spain, the picture serves to remind us that the continuity of a great empire ultimately comes down to just a few individuals in a room, and that they will pass. In presenting his argument that Spain is nothing less than "the place where the art and religions of east and west collided and where the nature of European culture and civilisation was decided", he started with the conflict between Islam and Catholicism, but it's a story that goes on to embrace other fundamental religious and political forces - protestantism, atheism, secularism, socialism and fascism. Velázquez's decisive contribution was to find the wonderful in the ordinary - and the ordinary in the awesome: as the Italian artist Luca Giordano put it, Las Meninas represents "the theology of painting".

Giordano in turn is a beneficiary of the Prado's redevelopment. His finest fresco in Spain, The Apotheosis of the Spanish Monarchy, adorns the ceiling of the nearby building known as the Casón del Buen Retiro, where it and 75 other works are currently on view (till May 4, admission free, not at the regular Prado times, but Wednesdays to Sundays, noon-8pm).

On the other side of the Paseo del Prado, the permanent collection of the Thyssen-Bornemisza Museum offers as fine a selection of European art from the last 700 years as you might see anywhere in an hour, and if you then set out in the direction of the Reina Sofía, you'll encounter a new kid on the block. The CaixaForum Madrid was designed by Tate Modern (and Beijing National Stadium) architects Jacques Herzog and Pierre de Meuron from Switzerland: on this occasion, they converted an electricity power station into an elegant red brick and corroded cast-iron "fortress", with an impressive 15,000-plant vertical garden running up a neighbouring wall.

To hold its own as a fourth point added to the art triangle with a relatively small exhibition space, it will need to focus on quality. The exhibition The Bread of Angels - what the body of Christ becomes according to the Catholic concept of transubstantiation - does that by featuring 45 works from the Uffizi Gallery in Florence, from Botticelli to Luca Giordano (till May 25, 10am-8pm, admission free). Giordano's On the Way Up to Calvary provides a variation of the formula he devised for Las Meninas: here we have the painting of theology, just one of the combinations of representation with belief, hope, alienation and despair to be found in a city where art so often leaves you speculating beyond the point where words are of much help.